摘要：
Statistical evolution of small fatigue crack behavior is analyzed. Three considerations are given. They consist of the total fit, the consistency of statistical parameters with test data, and the practice of commonly used distributions, namely Weibull (two- and three-parameters), normal, lognormal, extreme minimum, extreme maximum, and exponential. The crack growth rate data of 1Cr18Ni9Ti stainless steel-weld metal reveal that fatigue damage is a gradual process involving an initial non-ordered (chaotic) or load history-independent random state to an ordered load history-dependent random state. The seven distributions are examined. Different from existent conclusion, appropriate assumed distribution for characterizing the evolution data is the normal or extreme minimum value model rather than the Weibull two- or three-parameter. The other distributions do not fit the data as they violated two or all three of the mentioned considerations.

摘要：
A probabilistic assessment is made of the design S-N curves for 1Cr18Ni9Ti pipe-welded joint. The material exhibits a character of random cyclic stress-strain and fatigue life responses. Then, both the S and N in the virtual stress amplitude-fatigue crack initiation life (S-N) data are random variables. A general maximum likelihood method, which considers the randomness of the test S-N data, is developed to model the probabilistic S-N relations of material. The design S-N curves with reduction factors of 20 oil cycles, 2 on stress and 2.5 on stress applied to the best-fit S-N curve of test data as used in the ASME code and general practice, are assessed in a probabilistic sense. The results reveal that in the lower S regime the 20 and 2.5 reduction factor curves may be appropriate, while the reduction factor of 2 is slightly nonconservative. But in the higher S regime these curves are all much more conservative. The intrinsic cause is that the standard deviation of logN exhibits an increase with the S decreasing, while the constant reduction factors do not consider this increase. It is shown that from the general statistical scatter of S-N data the design S-N curves should be appropriately determined by a probabilistic approach.

摘要：
This paper pays special attention to an issue that there is a significant scatter of the stress-strain responses of a nuclear engineering material, 1Cr18Ni9Ti stainless steel pipe-weld metal. Efforts are made to reveal the random fatigue damage character by fracture surface observations and to model the random responses by introducing probability-based stress-strain curves of Ramberg-Osgood relation and its modified form. Results reveal that the fatigue damage is subjected to, 3-D interacting and involved microcracks. The three stages, namely microstructural short cracks (MSC), physical short cracks (PSC) and long cracks (LC) subdivided by Miller and de los Rios, can give a good characterization of the damage process. Both micro- and macro-behaviour of the material have the character of three stages. The 3-D effects are strong in the MSC stage, tend to a gradual decrease in the PSC stage, and then show saturation after going to the LC stage. Intrinsic causes of the random behaviour are the difference and evolution of the microstructural conditions ahead of the dominant crack tips. The 'effectively short fatigue crack criterion' introduced by Zhao et al. in observing the material surface short crack behaviour could facilitate an understanding of the mechanism of interaction and evolution. Based on the previous obtained appropriate assumed distribution, normal model, for the cyclic stress amplitude, the probability-based curves are approximated by the mean value and standard deviation cyclic stress-strain curves. Then, fatigue analysis at arbitrarily given reliability can be conveniently made according to the normal distribution function. To estimate these curves, a maximum likelihood method is developed. The analysis reveals that the curves could give a good modeling of the random responses of material. (C) 2000 Elsevier Science S.A. All rights reserved.

摘要：
The evolutionary density and the scatter of densities of the short fatigue cracks on the surface of 1Cr18Ni9Ti pipe-weld metal were observed by local and overall viewpoints, respectively. The local viewpoint, which is in accordance with a so-called effectively short fatigue crack criterion, paid attention to the dominant effective short fatigue crack (DESFC) initiation zone and the zones ahead of the DESFC tips. The overall viewpoint focused on the whole test piece of specimen. The results revealed that the density and scatter evolution exhibited significant characters of microstructural short crack stage and physical short crack stage. The evolutionary behavior by the local viewpoint was sensitive to the increase of the DESFC size and the translation of the tip location and showed a good agreement with the general observation results of DESFC acting gradually as a long crack and the scatter of DESFC growth rates tending gradually to that of a long crack . The intrinsic causes of the material random cyclic strain-life relations and stress-strain responses are appropriately given. In contrast, the evolutionary behavior by the overall viewpoint was non-sensitive and violated the general test observations. Therefore, the intrinsic localization and randomization of material evolutionary fatigue damage should be more appropriately revealed from the observations by the local viewpoint.

摘要：
An experimental study into microstructural effects on short fatigue crack behaviour of 19 stainless steel weld metal smooth specimens during low‐cycle fatigue is performed by a so‐called ‘effective short fatigue crack criterion’. This material has a mixed microstructure in which it is difficult to distinguish the grains and measure the grain diameter. The columnar grain structure is made up of matrix‐rich δ ferrite bands, and the distance between the neighbouring rich δ ferrite bands is an appropriate measurement for characterizing this structure. Particularly, the effective short fatigue cracks (ESFCs) always initiate from the bands of δ ferrite in the matrix in the weakest zone on one of the specimen surface zones which is orientated in accordance with the inner or outer surface of welded pipe from which the specimens were machined. These cracks exhibit characteristics of the microstructural short crack (MSC) and the physically small crack (PSC) stages. The average length of the ESFCs at the transition between MSC and PSC behaviour is ≈40 μm, while the corresponding fatigue life fraction is ≈0.3 at this transition. Different from previous test observations, the growth rate of the dominant effective short fatigue crack in the MSC stage still shows a decrease with fatigue cycling under the present low‐cycle fatigue loading levels. A statistical evolution analysis of the growth rates reveals that the short fatigue crack growth is a damage process that gradually evolves from a non‐ordered (chaotic) to a perfectly independent stochastic process, and then to an ordered (history‐dependent) stochastic state. Correspondingly, the microstructural effects gradually evolve from a weak effect to a strong one in the MSC stage, which maximizes at the transition point. In the PSC stage, the effects gradually evolve from a strong to weak state. This improves our understanding that the short crack behaviour in the PSC stage is mainly related to the loading levels rather than microstructural effects.

摘要：
This paper pays a special attention to the issue that there is a significant scatter of the stress-strain responses of a nuclear engineering material, 1Cr18Ni9Ti stainless steel pipe-weld metal. Statistical investigation is made to the cyclic stress amplitudes of this material. Three considerations are given. They consist of the total fit, the consistency with fatigue physics and the safety in practice of the seven commonly used statistical distributions, namely Weibull (two- and three-parameter), normal, lognormal, extreme minimum value, extreme maximum value and exponential. Results reveal that the data follow meanwhile the seven distributions but the local effects of the distributions yield a significant difference. Any of the normal, lognormal, extreme minimum value and extreme maximum value distributions might be an appropriate assumed distribution for characterizing the data. The normal and extreme minimum models are excellent. Other distributions do not fit the data as they violate two or three of the mentioned considerations.

摘要：
This paper develops an efficient reliability degrading model, referred to as a general isodegrading model, for mechanical equipment reliability and performance prediction under the PM (preventive maintenance) policy that the number of failures in each PM cycle should be kept as near as possible the same, the operational time in each PM cycle is maximized availability, and the equipment should be overhauled or scrapped on time when the economical benefit in a PM cycle is less than the demanded level. The core of the model is that there are isodegrading rates between neighbouring PM cycles for the equipment reliability and the performance parameters optimal operational time, MTBF, output and operational cyclic number, and there is an isodegrading speed between the parameters. This model, introducing an integrated measurement-general isodegrading rate gamma and an idea of demanded PM, has broken through the restriction that equipment nas the same maintenance time intervals and steady-state availability as in traditional models. It combines natural reliability degradation with performance degradation, and provides a scientific basis for the reliability and performance prediction of equipment both in operation and in development. The model is effectively applied in the determination of recommended PM criteria in the first over haul cycle of the gantry cranes used at railway terminals in China. The field inspection of the recommend criteria has proved that the general isodegrading model is practical and effective. (C) 1998 Elsevier Science Ltd. All rights reserved.

摘要：
Modeling of random cyclic strain-life (CSL) relations of engineering material should be a basis of strain-based fatigue reliability analysis. A statistical model for the relations of a nuclear engineering material, 1Cr18Ni9Ti stainless steel pipe-weld metal under temperature of 240 degreesC, is presented. In the model, a verified distribution, i.e. lognormal distribution, is used as an appropriate assumed distribution of the material fatigue life data. Based on the Coffin-Manson law, the relations are modeled by mean value- and standard deviation-cyclic curves of the logarithm of fatigue life. Then, fatigue analysis at an arbitrarily given probability can be made conveniently according to the normal distribution function. An approach for estimating the curves and their confidence bounds is developed by a linear regression technique. Different from the existent reliability analysis methods that considered the material constants in the law as independently random variables, present work treats them as dependently random variables from the fit of test data. Availability of the model has been indicated by an analysis of the material test data. (C) 2001 Elsevier Science B.V. All rights reserved.

摘要：
The size evolution of the surface short fatigue cracks of 1Cr18Ni9Ti weld metal was investigated. A local viewpoint is applied and found to be agreement with a so-called 'effectively short fatigue crack criterion'. Attention was paid to the dominant effectively short fatigue crack (DESFC) initiation zone and the zones ahead of the DESFC tips. The results reveal that the evolutionary size shows a significant character of microstructural short crack (MSC) and physical short crack (PSC) stages. In the MSC stage, the fatigue damage is due to mainly the initiation and the irregular growth of the effectively short fatigue cracks (ESFCs). In the PSC stage, the fatigue damage is conversely due to mainly the DESFC growth and partially, the growth of the ESFCs and the coalescence of the ESFCs themselves with the DESFC. The process involves from a non-ordered/chaotic state in the initiation of MSC stage, gradually to an independently random state at the transition point between the MSC and PSC stages and then, to an ordered/history-dependent random state. The interactive effect of the collective cracks is stronger and shows an increase in the MSC stage. It reaches a maximum value at the transition point and then, tends to the decrease in the PSC stage. The DESFC acts as a result of the interactive cracks and thus, is deemed suitable to describe the behaviour of collective cracks.

摘要：
Considering the factors such as the nonlinearity backlash, static transmission error and time-varying meshing stiffness, a three-degree-of-freedom torsional vibration model of spur gear transmission system for a typical locomotive is developed, in which the wheel/rail adhesion torque is considered as uncertain but bounded parameter. Meantime, the Ishikawa method is used for analysis and calculation of the time-varying mesh stiffness of the gear pair in meshing process. With the help of bifurcation diagrams, phase plane diagrams, Poincare maps, time domain response diagrams and amplitude-frequency spectrums, the effects of the pinion speed and stiffness on the dynamic behavior of gear transmission system for locomotive are investigated in detail by using the numerical integration method. Numerical examples reveal various types of nonlinear phenomena and dynamic evolution mechanism involving one-period responses, multi-periodic responses, bifurcation and chaotic responses. Some research results present useful information to dynamic design and vibration control of the gear transmission system for railway locomotive. (C) 2016 Elsevier Ltd. All rights reserved.

摘要：
The density and size of short cracks on the surface of 1Cr18Ni9Ti stainless steel smooth specimens during low cycle fatigue are investigated using a replica technique. The density and size data are analysed from two different observation policies, i.e. Policy I pays attention to the whole specimen test piece and Policy II is related to an ‘effective short fatigue crack criterion’, which pays attention to the dominant crack (DC) initiation zone and the zones ahead of the DC tips. The results reveal that both the crack density and crack size evolution exhibit a specific character during the microstructural short crack (MSC) and physical short crack (PSC) stages. The Policy I‐based observations exhibit an increasing density and little scatter of the density data. The increasing density violates the general test observation of decreasing collective crack effects in the PSC stage. The little scatter is too small to reflect the intrinsic scatter of fatigue properties. Both the crack density and crack size evolution from this policy show little relationship with the intrinsic localization of fatigue damage. However, Policy II‐based observations show an increasing crack density and an increasing density scatter in the MSC stage. The density and scatter reach their maximum values at the transition point between the MSC and PSC stages. Then, they decrease with fatigue cycling in the PSC stage and tend to their saturation values when the DC size is above about 500 μm. This behaviour shows a good agreement with the general test observations of decreasing collective crack effects and growth rate scatter in the PSC stage. Further, both approaches exhibit an evolutionary positively skewed crack size distribution, and an increasing difference between the average crack length and the DC length in the PSC stage, indicative of decreasing collective crack effects. A three‐parameter Weibull distribution (3‐PWD) is appropriately used to describe the crack sizes and a 6.5 to 7.6 μm value of location parameter of the distribution is obtained to reflect a minimum value for the initial cracks. It is worth noting that Policy I‐based observations show an increasing positively skewed crack size distribution, an increasing scatter of the size data and a decreasing shape parameter of the 3‐PWD. This represents an increasing collective crack effect and an increasing irregularity of interactive cracks, which violates the general test observations. In contrast, Policy II‐based observations exhibit a decreasing positively skewed size distribution shape and an increasing (from <1 gradually to >1) shape parameter of the 3‐PWD that is in agreement with the general test observations. The increasing shape parameter indicates that the collective crack effects act as an evolutionary process from an initial non‐ordered (chaotic) random state gradually to an independent random state at the transition point between the MSC and PSC stages and then, to a loading history‐dependent random state. This behaviour is in accordance with the evolutionary DC growth behaviour. Therefore, the evolutionary short crack behaviour associated with the intrinsic localization of fatigue damage should be appropriately revealed from the ‘effective short fatigue crack criterion’‐based observations.